σ Standard Deviation Calculator
Standard deviation measures spread: how far numbers typically stray from the average. A low value means the data clusters tightly; a high value means it is all over the place. It is the backbone of statistics, quality control and risk analysis.
Paste your numbers separated by commas, spaces or line breaks. You get both the population version (your data is everything) and the sample version (your data is a subset) — use sample when generalizing beyond the numbers you entered.
How to use this calculator
Paste your numbers into the box, separated by commas, spaces or line breaks. You get the mean, variance and standard deviation - both population and sample versions.
- Paste or type your numbers into the Numbers box, separating them with commas, spaces or line breaks.
- Enter at least two numbers - a single value has no meaningful spread.
- Press Calculate to see the mean, both standard deviations and both variances.
- Add or remove values and recalculate to watch how outliers move the standard deviation.
Frequently asked questions
What does this calculator report?
It summarizes any dataset: count, mean, population and sample variance, population and sample standard deviation, and the minimum and maximum. The mean is shown as the headline result.
How is standard deviation calculated?
It first finds the mean, then averages the squared distances of each value from the mean - that average is the variance, and the square root of the variance is the standard deviation. Dividing by n gives the population version; dividing by n - 1 gives the sample version.
Can you show a worked example?
Enter 2, 4, 4, 4, 5, 5, 7, 9. The mean is 5, and the population standard deviation is exactly 2 - a tidy textbook example showing moderate spread around the mean.
Should I use the population or sample version?
Use the sample version when your numbers are a subset drawn from something larger, such as a survey. Use the population version when your numbers are the entire group you care about. One extreme outlier will inflate the standard deviation noticeably, so glance at the min and max first.